Question 4. If a projectile is shot up a hill, the distance (range) of the landing point up the hill depends on the initial speed of the projectile, v, the angle of inclination of the hill, @, and the angle of elevation of the gun, 0. The range of the projectile, in meters, is given by the formula R = 2v2 [ sin(0 - a) cos 0 ] g cos' a where g is the gravitational field strength, in m/s (a) Determine the value of 0 that maximizes the range for a hill with an angle of inclination (b) Calculate the range for this angle, if the initial speed of the projectile is 50 m /s and g = 9.8 m/s Round your final answer to a whole number. Question 5. Consider the functions f(x) = (2e) and g(x) - (2 . e). For each function, is the graph of the derivative of the function above, below, or the same as the graph of the function? Explain 2+ 2er Question 6. Consider the function f (2) - 3 + 2ex (a) Is f(ze) always increasing? Explain (b) How many horizontal asymptotes does f(x) have? Determine the equations if any. (c) Use your answers from part (a) and (b) to sketch the graph of f (ae)